Consider the following game. Terry and Kerry are roommates who must make decisions about cleaning simultaneously. Terry’s payoff is the first number in each cell and a higher number is a better outcome:

Kerry

Clean

Don’t clean

Terry

Clean

( 8, 2 )

( 3, 5 )

Don’t clean

( 10, 3 )

( 4, 1 )

Question

Consider the following game. Terry and Kerry are roommates who must make decisions about cleaning simultaneously. Terry’s payoff is the first number in each cell and a higher number is a better outcome:

Kerry

Clean

Don’t clean

Terry

Clean

( 8, 2 )

( 3, 5 )

Don’t clean

( 10, 3 )

( 4, 1 )

BlackTom AI · Accepted Answer

Begin by restating the scenario in my own words to set the stage for evaluating dominance across Terry and Kerry's choices.
Option A: Only Terry has a strictly dominant strategy. To check this, compare Terry's payoffs for each of Kerry's possible actions. If Kerry cleans, Terry gets 8 by cleaning and 10 by not cleaning; if Kerry does not clean, Terry gets 3 by cleaning and 4 by not cleaning. In both cases, 'Don’t Clean' yields a higher payoff for Terry, so Terry has a strictly dominant strategy: Don’t Clean. This makes Option A plausible as the correct description of the game.
Option B: Only Kerry has a strictly dominant strategy. Examine Kerry’s payoffs across Terry’s two possible actions. When Terry cleans, Kerry gets 2 if she cleans and 5 if she doesn’t clean; when Terry doesn’t clean, Kerry gets 3 if she cleans and 1 if she doesn’t clean. There is no single Kerry strategy that outperforms the other in all of Terry’s actions (Clean dominates Don’t Clean only for one of Terry’s actions, while Don’t Clean dominates Clean for the other). Therefore Kerry does not have a strictly dominant strategy, so Option B is incorrect.
Option C: Both Terry and Kerry have a strictly dominant strategy. Since we just established Kerry lacks a dominant strategy, this option cannot be true. There cannot be mutual dominance here.
Option D: Neither Terry nor Kerry have a strictly dominant strategy. This would be true if both players lacked a dominating move, but Terry clearly has Don’t Clean as a strictly dominant choice regardless of Kerry’s action, making this statement false.
Option E: None of the above. Given that Option A correctly identifies Terry’s strictly dominant strategy, this option is not accurate.
In summary, the correct interpretation is that Terry has a strictly dominant strategy (Don’t Clean), while Kerry does not have one, which supports Option A as the valid choice. The other options either overstate Kerry’s situation, claim mutual dominance, or deny Terry’s dominance, all of which contradict the payoff structure provided.

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